CN117375037B - Mobile energy storage system scheduling method based on voltage sensitivity analysis - Google Patents

Mobile energy storage system scheduling method based on voltage sensitivity analysis Download PDF

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CN117375037B
CN117375037B CN202311663854.3A CN202311663854A CN117375037B CN 117375037 B CN117375037 B CN 117375037B CN 202311663854 A CN202311663854 A CN 202311663854A CN 117375037 B CN117375037 B CN 117375037B
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吴婷
庄恒
黄祁生
王怀智
朱荣伍
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Harbin Institute Of Technology shenzhen Shenzhen Institute Of Science And Technology Innovation Harbin Institute Of Technology
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Abstract

The invention discloses a mobile energy storage system dispatching method based on voltage sensitivity analysis, which belongs to the technical field of mobile energy storage system dispatching and comprises the following steps: s1, generating a day-ahead scheduling scheme of a power distribution network based on prediction data; s2, acquiring probability distribution of node voltage of a power distribution network in a day-ahead scheduling scheme based on voltage sensitivity analysis; s3, taking the voltage out-of-limit probability of each node, the charge state of each mobile energy storage system and the time required for the mobile energy storage system to reach the corresponding point into consideration, and screening out the total route of the mobile energy storage system for 24 hours in the future; s4, constructing an optimal path navigation model of the mobile energy storage system based on traffic flow data; s5, constructing an optimal power output generation model of the mobile energy storage system based on the real-time load condition. By adopting the mobile energy storage system scheduling method based on voltage sensitivity analysis, the travel time of the mobile energy storage system can be reduced, and the destination of the mobile energy storage system can be reasonably arranged.

Description

Mobile energy storage system scheduling method based on voltage sensitivity analysis
Technical Field
The invention relates to the technical field of mobile energy storage system scheduling, in particular to a mobile energy storage system scheduling method based on voltage sensitivity analysis.
Background
With the continued development and popularity of renewable energy sources, intermittent renewable energy sources, including solar and wind energy, are gradually penetrating into power distribution grids. However, the instability and volatility of such renewable energy sources presents a number of challenges to the operation of the distribution network. In this context, energy storage systems will be indispensable in future low-carbon oriented energy systems to accommodate the high permeability of distributed power sources. However, conventional stationary energy storage systems suffer from the economic disadvantages of intermittent revenue streams and low utilization. In recent years, as traffic electrification progresses, the concept of a portable power source has been developed. The mobility of the mobile power source enhances its ability to mine multiple value streams with temporal and spatial variability, as compared to a stationary energy storage system, thereby improving its asset utilization and potential value proposition.
Therefore, the scheduling strategy of the mobile energy storage system becomes an important issue.
Disclosure of Invention
The invention aims to provide a mobile energy storage system scheduling method based on voltage sensitivity analysis, which can reduce travel time of a mobile energy storage system, improve voltage distribution of a power distribution network, reduce the influence of errors of load prediction on the stability of a power system and reasonably arrange a destination of the mobile energy storage system.
In order to achieve the above purpose, the invention provides a mobile energy storage system scheduling method based on voltage sensitivity analysis, which comprises the following steps:
s1, generating a day-ahead scheduling scheme of a power distribution network based on prediction data;
s2, aiming at the day-ahead scheduling scheme generated in the step S1, calculating probability distribution of voltage values of each node at each moment in consideration of prediction errors;
s3, aiming at probability distribution of the voltage values obtained in the step S2, generating a route of the mobile energy storage system for 24 hours in the future by taking the probability of voltage out-of-limit, the charge state of each mobile energy storage system and the time required for the mobile energy storage system to reach a corresponding point into consideration;
s4, aiming at the route in the step S3, considering traffic flow data, and constructing an optimal path navigation model of all the mobile energy storage systems;
s5, aiming at the optimal path navigation model constructed in the step S4, taking real-time load conditions into consideration, and constructing an optimal power output generation model of the mobile energy storage system.
Preferably, in step S1, a day-ahead scheduling scheme of the power distribution network is generated based on the prediction data, which specifically includes: the method comprises the steps of adopting predicted load data, considering original equipment of a power distribution network, and obtaining output of the original equipment of the power distribution network by utilizing an optimal power flow calculation model; the objective function of the optimal power flow calculation model is as follows:
（1）
wherein,Nrepresenting a collection of points in the distribution network equipped with generators,is an electric generatornRunning costs of->Representative generatornOutput power;
constraint conditions of the optimal power flow model are as follows:
(1) The voltage of a certain node is expressed as the voltage of the node adjacent to the certain node minus the voltage drop caused by the branch current on the branch; the non-convex node voltage transfer constraint is convex by removing the phase angles of the current and the voltage, reserving the amplitude and expressing the square of the current by a primary term:
（2）
wherein,v i representative nodeiA voltage amplitude;v j representative nodejA voltage amplitude;R ij is a nodeijResistance values therebetween;X ij is a nodeijReactance value between;P ij is a nodejInflow nodeiIs a power of (2);Q ij is a nodeiInflow nodejReactive power in between;l ij,t is a nodeijThe square of the current amplitude between them; omega is the set of grid nodes,i，jrepresenting nodes in the network;
(2) The power of the ingress node is equal to the power of the egress node; the power balance constraint is relaxed by splitting active power and reactive power:
（3）
（4）
wherein,active power for the inflow node; />Reactive power for the inflow node; />Slave nodeiOut to the nodekIs a power of (2); />Representing nodes in a networkiA collection of connected nodes; />Representing slave nodesjInflow to nodeiIs a power of (2); />Representative nodejiResistance values therebetween; />Representative nodejFlow direction nodeiIs the square of the current amplitude of (2); />Representing slave nodesiOut to the nodekIs set in the power domain; />Representing slave nodesjInflow to nodeiIs set in the power domain; />Representative nodejSum nodeiReactance value between;i，j，kall represent nodes in the network; />The output power of the generator at the node i;
(3) The square of the branch current is equal to the modular square of the apparent power divided by the node voltage; second order cone relaxation is carried out on branch power flow calculation constraint:
（5）
wherein,representing slave nodesiFlow direction nodejIs the square of the current amplitude of (2);
(4) The node voltage should satisfy the voltage constraint:
（6）
wherein,representative nodeiA lower voltage limit of (2); />Representative nodeiUpper voltage limit of (2);
(5) The branch current should satisfy the current constraint:
（7）
wherein,representative nodeiTo the nodejAn upper limit of the square of the current magnitude of (2);
(6) The power distribution network generator should meet the generator output constraint:
（8）
wherein,representative nodeiThe upper power limit of the generator; />Representative nodeiAt the lower power limit of the generator.
Preferably, in step S2, for the day-ahead scheduling scheme generated in step S1, a probability distribution of voltage values of each node at each time is calculated in consideration of a prediction error, and the method includes the following steps:
s21, calculating the variation of the voltage of the network node caused by the power variation;
the node connecting large power grid in power distribution network is called source node, and is used as letterSA representation; the node for observing the voltage change is called an observation node and is marked with lettersORepresenting, then observe the voltage at the nodeV O Expressed as the voltage at the source nodeV S A difference from a sum of voltage drops on all sides between the observation node and the source node; by kirchhoff's voltage law, the voltage at the observation node is expressed as:
（9）
wherein,U b representative is in the branchbVoltage drop of (2); omega shape branch Is a collection of edges between a source node and an observation node;
is arranged at the nodeiThe complex power of injection isS i At the nodeiThe voltage complex conjugate at isThe set of nodes between the source node and the observation node isN node The injection power of the intermediate node is changed to +.>The voltage of the intermediate node is changed to +.>Then observe the voltage change delta of the nodeV O Expressed as:
（10）
wherein,representing the voltage value after the change of the observation node; />A complex conjugate representing a voltage change at the intermediate node;impedance between source node and observation node;
considering that the voltage phase angle change of the power distribution network is small, loosening the voltage in the equation, reserving amplitude information, and obtaining the upper limit of the node voltage change quantity of the power distribution network:
（11）
wherein,N action as a set of nodes of varying power,Z oi for the impedance shared between the source node to the action node and the observation node,representative nodeiPower variation of (2);
s22, calculating probability distribution of node voltage values;
considering that the error of the prediction system is normal distribution, and the influence of the active power and reactive power changes among different nodes is expressed as a covariance matrix; because the phase angle change of the power distribution network is small, the probability distribution of the voltage amplitude change is considered; the square of the amplitude of the voltage is expressed as the sum of squares of a real part and an imaginary part, and since the prediction error is normally distributed, the distribution of the square of the amplitude of the voltage is a weighted sum of squares of normal distribution and is expressed by gamma distribution; the probability of the node voltage change of the distribution network is calculated by the following formula:
（12）
wherein,a reference value representing a node voltage variation amount;βandθthe shape parameter and the scale parameter of the gamma distribution are calculated by the following formula:
（13）
wherein, the mathematical expectation and variance are the eigenvalues of the covariance matrixAnd->And (3) calculating to obtain:
（14）
（15）。
preferably, in step S3, for the probability distribution of the voltage values obtained in step S2, a route of 24 hours in the future of the mobile energy storage system is generated by taking into account the probability of voltage out-of-limit, the state of charge of each mobile energy storage system, and the time required for the mobile energy storage system to reach the corresponding point, including the following steps:
s31, grouping out-of-limit points;
s32, calculating a set of points which can be reached by the mobile energy storage in fixed time;
s33, calculating the charge state of the mobile energy storage system;
s34, generating a total route of the mobile energy storage system.
Preferably, step S31 specifically includes: and (2) calculating the probability of voltage out-of-limit of each node based on the node voltage probability density function obtained in the step (S2), and dividing the probability into two groups of points which are an upper limit point and a lower limit point.
Preferably, step S32 specifically includes: constructing an optimal path selection model considering the shortest travel time, wherein the objective function of the model is as follows:
（16）
wherein,representing the time the mobile energy store navigates between destinations;
the constraint conditions of the optimal path selection model are as follows:
(1) The travel time of the mobile energy storage system between destinations is equal to the sum of the time it takes to walk through all road segments:
（17）
wherein,binary variables representing a selected section of the road network, which is then +.>The method comprises the steps of carrying out a first treatment on the surface of the When the mobile energy storage system does not pass through the road section ∈>；/>At the node for MESSijTime spent navigating in between;
(2) All road sections through which the mobile energy storage system passes should be connected end to end, and for a starting point, the mobile energy storage system can only exit from the point; for an intermediate node, the mobile energy storage system should only drive in to the point once and only drive out of the point once; for an endpoint, the mobile energy storage system can only exit the point once:
（18）
wherein,Hrepresenting the start of the overall route;Drepresenting the end of the total route;representing a set of road network nodes; />For the binary variable of a road network selection section, when the mobile energy storage system passes the section, there is +.>The method comprises the steps of carrying out a first treatment on the surface of the When the mobile energy storage system does not pass through the road section ∈>；/>And->Is opposite to the direction of (3);
according to the obtained optimal path selection model, sequentially scanning road network nodes, calculating an endpoint set with the shortest travel time of each node being less than 15 minutes and 30 minutes, and recording as D 15min And D 30min 。
Preferably, step S33 specifically includes: the state of charge transfer equation of the mobile energy storage system is:
（19）
wherein,representing mobile energy storage systemmAt the moment of timetIs a state of charge of (2); />Representing mobile energy storage systemmAt the moment of timetIs a power output of (a);trepresenting a charging time of the mobile energy storage system; />Representing the maximum capacity of the mobile energy storage system battery; />Representing the aggregate of all mobile energy storage systems.
Preferably, step S34 specifically includes: meanwhile, the following steps are executed by considering the high probability out-of-limit point of the power grid, the point which can be reached quickly by the mobile energy storage system and the charge state of each mobile energy storage system:
s341 rootThe upper limit point and the lower limit point obtained in the step S31 are respectively equal to D 15min Taking the intersection to obtain selectable destinations of two groups of mobile energy storage systems which are divided into an upper limit and a lower limit; considering the extreme case that all mobile energy storage systems need to be charged or discharged, if the number of points in the obtained intersection is smaller than the number of the mobile energy storage systems, considering the point of the power grid which is easy to be out of limit in the next period, and D 30min Taking the intersection as a supplement of the destination of the mobile energy storage system at the current moment; generating a selectable destination sequence of the mobile energy storage system in 24 hours by a method of preferentially selecting current nodes and supplementing future nodes;
s342, according to the selectable destination sequence obtained in the step S341, considering the real-time state of charge of the mobile energy storage system, and for the mobile energy storage system with the state of charge lower than 50%, selecting a node with the highest probability of exceeding the upper voltage limit in the selectable destination sequence as a destination; for a mobile energy storage system with a charge state higher than 50%, selecting a node with the highest probability of exceeding a lower voltage limit in an optional destination sequence as a destination; eventually a total route is generated for each mobile energy storage system for the next 24 hours.
Preferably, step S4 specifically includes: according to the mobile energy storage total route obtained by calculation in the step S3, considering the influence of real-time traffic flow, comprehensively considering the minimized fuel cost and the time cost, constructing an online optimal path navigation model of the mobile energy storage system, and the objective function of the model is as follows:
（20）
wherein,fuel consumption for the mobile energy storage system; />Representing the time taken by the mobile energy storage system in providing power support; />Representing the weight of the time cost in the objective function;
the partial constraint condition of the online optimal path navigation model of the mobile energy storage system is the same as the constraint condition of the optimal path selection model in the step S32, and the newly added constraint condition is as follows:
(1) The navigation time of the mobile energy storage system in each road section is affected by real-time traffic flow, and the navigation time of the traffic flow is considered to be expressed as a BRP model:
（21）
wherein the method comprises the steps ofRepresenting the navigation time under the influence of traffic flow; />Representing free sailing time of the mobile energy storage system under no influence of traffic flow; />Representing real-time traffic flow;d，b，Cis a preset parameter;
(2) The fuel cost of the mobile energy storage system is affected by the length of the sailing distance and the price of fuel oil:
（22）
wherein,representing the price of fuel; />Representing the amount of fuel consumed per kilometer; />Representing individual road segments in a networkLength.
Preferably, step S5 specifically includes: based on real-time load data, an optimal power output generation model of the mobile energy storage system is built, the output power of each mobile energy storage system is calculated, and an objective function of the model is as follows:
（23）
wherein,cost of providing power support on behalf of the mobile energy storage system; />Representing at the nodeiMobile energy storage systemmOutput power of (2); />Representative generatornIs not limited by the operating cost of (a);
the partial constraint condition of the optimal power output generation model is the same as the optimal power flow calculation model in the step S1, and the newly added constraint condition is as follows:
(1) The power output of a mobile energy storage system will bring about a change in its state of charge:
（24）
(2) The output power of the mobile energy storage system should satisfy the power constraint:
（25）
wherein,for moving energy-storage systemsmLower power limit of (2); />For storing energy for movementmUpper power limit of (2); />For storing energy for movementmOutput power of (2);
(3) The power injection of the mobile energy storage system affects the power balance equation of the node:
（26）。
therefore, by adopting the mobile energy storage system scheduling method based on the voltage sensitivity analysis, the travel time of the mobile energy storage system can be reduced, the voltage distribution of the power distribution network can be improved, the influence of the error of load prediction on the stability of the power system can be reduced, and the destination of the mobile energy storage system can be reasonably arranged.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a schematic flow chart of a mobile energy storage system scheduling method implementation based on voltage sensitivity analysis of the present invention;
FIG. 2 is a schematic flow chart of an electric vehicle charging station planning method implemented by a mobile energy storage system scheduling method based on voltage sensitivity analysis of the present invention;
fig. 3 is a schematic overall view of a mobile energy storage system dispatching method implemented by the mobile energy storage system dispatching method based on voltage sensitivity analysis.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs.
Example 1
Referring to fig. 1, a flow chart of a mobile energy storage system dispatching method based on voltage sensitivity analysis according to the present invention specifically includes the following steps:
s1, generating a day-ahead scheduling scheme of a power distribution network based on prediction data;
the method comprises the steps of adopting predicted load data, considering original equipment of a power distribution network, and obtaining output of the original equipment of the power distribution network by utilizing an optimal power flow calculation model; the objective function of the optimal power flow calculation model is as follows:
（1）
wherein,Nrepresenting a collection of points in the distribution network equipped with generators,is an electric generatornRunning costs of->Representative generatornOutput power;
constraint conditions of the optimal power flow model are as follows:
(1) The voltage of a certain node is expressed as the voltage of the node adjacent to the certain node minus the voltage drop caused by the branch current on the branch; the non-convex node voltage transfer constraint is convex by removing the phase angles of the current and the voltage, reserving the amplitude and expressing the square of the current by a primary term:
（2）
wherein,v i representative nodeiA voltage amplitude;v j representative nodejA voltage amplitude;R ij is a nodeijResistance values therebetween;X ij is a nodeijReactance value between;P ij is a nodejInflow nodeiIs a power of (2);Q ij is a nodeiInflow nodejReactive power in between;l ij,t is a nodeijThe square of the current amplitude between them; omega is the set of grid nodes,i，jrepresenting nodes in the network;
(2) The power of the ingress node is equal to the power of the egress node; the power balance constraint is relaxed by splitting active power and reactive power:
（3）
（4）
wherein,active power for the inflow node; />Reactive power for the inflow node; />Slave nodeiOut to the nodekIs a power of (2); />Representing nodes in a networkiA collection of connected nodes; />Representing slave nodesjInflow to nodeiIs a power of (2);representative nodejiResistance values therebetween; />Representative nodejFlow direction nodeiIs the square of the current amplitude of (2); />Representing slave nodesiOut to the nodekIs set in the power domain; />Representing slave nodesjInflow to nodeiIs set in the power domain; />Representative nodejSum nodeiReactance value between;i，j，kall represent nodes in the network; />Is a nodeiThe output power of the generator;
(3) The square of the branch current is equal to the modular square of the apparent power divided by the node voltage; second order cone relaxation is carried out on branch power flow calculation constraint:
（5）
wherein,representing slave nodesiFlow direction nodejIs the square of the current amplitude of (2);
(4) The node voltage should satisfy the voltage constraint:
（6）
wherein,representative nodeiA lower voltage limit of (2); />Representative nodeiUpper voltage limit of (2);
(5) The branch current should satisfy the current constraint:
（7）
wherein,representative nodeiTo the nodejAn upper limit of the square of the upper clipping value of the current;
(6) The power distribution network generator should meet the generator output constraint:
（8）
wherein,representative nodeiThe upper power limit of the generator; />Representative nodeiAt the lower power limit of the generator.
S2, aiming at the day-ahead scheduling scheme generated in the step S1, calculating probability distribution of voltage values of each node at each moment in consideration of prediction errors;
s21, calculating the variation of the voltage of the network node caused by the power variation;
the node connecting large power grid in power distribution network is called source node, and is used as letterSA representation; the node for observing the voltage change is called an observation node and is marked with lettersORepresenting, then observe the voltage at the nodeV O Expressed as the voltage at the source nodeV S A difference from a sum of voltage drops on all sides between the observation node and the source node; by kirchhoff's voltage law, the voltage at the observation node is expressed as:
（9）
wherein,U b representative is in the branchbVoltage drop of (2); omega shape branch Is a collection of edges between a source node and an observation node;
is arranged at the nodeiThe complex power of injection isS i At the nodeiThe voltage complex conjugate at isThe set of nodes between the source node and the observation node isN node The injection power of the intermediate node is changed to +.>The voltage of the intermediate node is changed to +.>Then observe the voltage change delta of the nodeV O Expressed as:
（10）
wherein,representing the voltage value after the change of the observation node; />A complex conjugate representing a voltage change at the intermediate node; />Impedance between source node and observation node;
considering that the voltage phase angle change of the power distribution network is small, loosening the voltage in the equation, reserving amplitude information, and obtaining the upper limit of the node voltage change quantity of the power distribution network:
（11）
wherein,N action as a set of nodes of varying power,Z oi for the impedance shared between the source node to the action node and the observation node,representative nodeiPower variation of (2);
s22, calculating probability distribution of node voltage values;
considering that the error of the prediction system is normal distribution, and the influence of the active power and reactive power changes among different nodes is expressed as a covariance matrix; because the phase angle change of the power distribution network is small, the probability distribution of the voltage amplitude change is considered; the square of the amplitude of the voltage is expressed as the sum of squares of a real part and an imaginary part, and since the prediction error is normally distributed, the distribution of the square of the amplitude of the voltage is a weighted sum of squares of normal distribution and is expressed by gamma distribution; the probability of the node voltage change of the distribution network is calculated by the following formula:
（12）
wherein,a reference value representing a node voltage variation amount; beta and theta are the shape parameter and the scale parameter of the gamma distribution, respectively, and are calculated by the following formula:
（13）
wherein, the mathematical expectation and variance are the eigenvalues of the covariance matrixAnd->And (3) calculating to obtain:
（14）
（15）。
s3, aiming at probability distribution of the voltage values obtained in the step S2, generating a route of the mobile energy storage system for 24 hours in the future by taking the probability of voltage out-of-limit, the charge state of each mobile energy storage system and the time required for the mobile energy storage system to reach a corresponding point into consideration;
s31, grouping out-of-limit points;
based on the node voltage probability density function obtained in the step S2, calculating the probability of each node voltage out-of-limit, and dividing the probability into two groups of points which are an upper limit point and a lower limit point
S32, calculating a set of points which can be reached by the mobile energy storage in fixed time;
constructing an optimal path selection model considering the shortest travel time, wherein the objective function of the model is as follows:
（16）
wherein,representing the time the mobile energy store navigates between destinations;
the constraint conditions of the optimal path selection model are as follows:
(1) The travel time of the mobile energy storage system between destinations is equal to the sum of the time it takes to walk through all road segments:
（17）
wherein,binary variables representing a selected section of the road network, which is then +.>The method comprises the steps of carrying out a first treatment on the surface of the When the mobile energy storage system does not pass through the road section ∈>；/>At the node for MESSijTime spent navigating in between;
(2) All road sections through which the mobile energy storage system passes should be connected end to end, and for a starting point, the mobile energy storage system can only exit from the point; for an intermediate node, the mobile energy storage system should only drive in to the point once and only drive out of the point once; for an endpoint, the mobile energy storage system can only exit the point once:
（18）
wherein,Hrepresenting the start of the overall route;Drepresenting the end of the total route;representing a set of road network nodes; />For the binary variable of a road network selection section, when the mobile energy storage system passes the section, there is +.>The method comprises the steps of carrying out a first treatment on the surface of the When the mobile energy storage system does not pass through the road section ∈>；/>And->Is opposite to the direction of (3);
according to the obtained optimal path selection model, sequentially scanning road network nodes, calculating an endpoint set with the shortest travel time of each node being less than 15 minutes and 30 minutes, and recording as D 15min And D 30min 。
S33, calculating the charge state of the mobile energy storage system;
the state of charge transfer equation of the mobile energy storage system is:
（19）
wherein,representing mobile energy storage systemmAt the moment of timetIs a state of charge of (2); />Representing mobile energy storage systemmAt the moment of timetIs a power output of (a);trepresenting a charging time of the mobile energy storage system; />Representing the maximum capacity of the mobile energy storage system battery; />Representing the aggregate of all mobile energy storage systems.
S34, generating a total route of the mobile energy storage system.
Meanwhile, the following steps are executed by considering the high probability out-of-limit point of the power grid, the point which can be reached quickly by the mobile energy storage system and the charge state of each mobile energy storage system:
s341, respectively comparing the upper limit point and the lower limit point obtained in the step S31 with D 15min Taking intersection to obtain alternative destinations of two groups of mobile energy storage systems divided into upper limit and lower limitThe method comprises the steps of carrying out a first treatment on the surface of the Considering the extreme case that all mobile energy storage systems need to be charged or discharged, if the number of points in the obtained intersection is smaller than the number of the mobile energy storage systems, considering the point of the power grid which is easy to be out of limit in the next period, and D 30min Taking the intersection as a supplement of the destination of the mobile energy storage system at the current moment; generating a selectable destination sequence of the mobile energy storage system in 24 hours by a method of preferentially selecting current nodes and supplementing future nodes;
s342, according to the selectable destination sequence obtained in the step S341, considering the real-time state of charge of the mobile energy storage system, and for the mobile energy storage system with the state of charge lower than 50%, selecting a node with the highest probability of exceeding the upper voltage limit in the selectable destination sequence as a destination; for a mobile energy storage system with a charge state higher than 50%, selecting a node with the highest probability of exceeding a lower voltage limit in an optional destination sequence as a destination; eventually a total route is generated for each mobile energy storage system for the next 24 hours.
S4, aiming at the route in the step S3, considering traffic flow data, and constructing an optimal path navigation model of all the mobile energy storage systems;
according to the mobile energy storage total route obtained by calculation in the step S3, considering the influence of real-time traffic flow, comprehensively considering the minimized fuel cost and the time cost, constructing an online optimal path navigation model of the mobile energy storage system, and the objective function of the model is as follows:
（20）
wherein,fuel consumption for the mobile energy storage system; />Representing the time taken by the mobile energy storage system in providing power support; />Representing the cost of timeWeights in the objective function;
the partial constraint condition of the online optimal path navigation model of the mobile energy storage system is the same as the constraint condition of the optimal path selection model in the step S32, and the newly added constraint condition is as follows:
(1) The navigation time of the mobile energy storage system in each road section is affected by real-time traffic flow, and the navigation time of the traffic flow is considered to be expressed as a BRP model:
（21）
wherein the method comprises the steps ofRepresenting the navigation time under the influence of traffic flow; />Representing free sailing time of the mobile energy storage system under no influence of traffic flow; />Representing real-time traffic flow; d, b, C is a preset parameter;
(2) The fuel cost of the mobile energy storage system is affected by the length of the sailing distance and the price of fuel oil:
（22）
wherein,representing the price of fuel; />Representing the amount of fuel consumed per kilometer; />Representing the length of each road segment in the network.
S5, aiming at the optimal path navigation model constructed in the step S4, taking real-time load conditions into consideration, and constructing an optimal power output generation model of the mobile energy storage system.
Based on real-time load data, an optimal power output generation model of the mobile energy storage system is built, the output power of each mobile energy storage system is calculated, and an objective function of the model is as follows:
（23）
wherein,cost of providing power support on behalf of the mobile energy storage system; />Representing at the nodeiMobile energy storage systemmOutput power of (2); />Representative generatornIs not limited by the operating cost of (a);
the partial constraint condition of the optimal power output generation model is the same as the optimal power flow calculation model in the step S1, and the newly added constraint condition is as follows:
(1) The power output of a mobile energy storage system will bring about a change in its state of charge:
（24）
(2) The output power of the mobile energy storage system should satisfy the power constraint:
（25）
wherein,for movingDynamic energy storage systemmLower power limit of (2); />For storing energy for movementmUpper power limit of (2); />For storing energy for movementmOutput power of (2);
(3) The power injection of the mobile energy storage system affects the power balance equation of the node:
（26）。
from the description, the scheduling method can find out the high probability voltage out-of-limit point in the power grid under the condition of inaccurate load data, so that the power distribution network has more robustness in operation and stronger capability of resisting uncertainty risks.
As shown in fig. 2, a specific method for generating an operation route of the mobile energy storage system in this embodiment includes the steps of:
(1) Acquiring probability distribution of voltage out-of-limit points, and classifying the probability distribution into D according to the voltage out-of-limit categories upper And D lower Two sets of data;
(2) Calculating a node set D which can be reached within 15 minutes and 30 minutes of each node in the road network 15min And D30 min ；
(3) Will D upper And D lower Respectively sum D 15min Taking intersection to obtain set D of points which can be reached quickly by mobile energy storage qu And D ql ；
(4) Judgment D qu And D ql If the data dimension is smaller than the number of the mobile energy storage systems, it is indicated that, in the extreme case that the mobile energy storage system can only be charged or discharged, some of the mobile energy storage systems are in a stagnation state. Consider D to be upper And D lower Respectively sum D 30min Taking intersection, and comparing D according to probability qu And D ql Supplement to moveThe energy storage system can be in standby state in advance until the node which is possibly out of limit in the next time period;
(5) If the data dimension is larger than the number of the mobile energy storage systems, respectively from D based on the number of the mobile energy storage systems qu And D ql And taking out the corresponding quantity of data to serve as an alternative node of the route of the mobile energy storage system.
(6) Calculating the state of charge of the mobile energy storage system, and selecting to go to D if the state of charge is lower than 50% qu In (c) and vice versa to D ql The high probability point of the mobile energy storage system is ensured to maintain the electric quantity of the mobile energy storage system to be about 50%, and the utilization rate is improved.
(7) Generating a total route of intended movement of the mobile energy storage system by continuing the backward calculation on the timeline.
In this embodiment, in order to process uncertainty factors caused by load prediction errors, voltage sensitivity analysis is first adopted to calculate voltage distribution of a power distribution network, probability of out-of-limit voltage of different nodes is obtained, and then a total route of expected movement of the mobile energy storage system is generated according to navigation time and state of charge of the mobile energy storage system.
As shown in fig. 3, a specific method for scheduling a mobile energy storage system based on voltage sensitivity analysis in this embodiment includes the steps of:
(a) Generating a day-ahead scheduling scheme of the power distribution network based on the prediction data;
(b) Calculating probability distribution of voltage values of each node at each moment by considering prediction errors according to the scheme generated in the step (a);
(c) Generating a route of the mobile energy storage system for 24 hours in the future by considering the probability of voltage out-of-limit, the charge state of each mobile energy storage system and the time required for the mobile energy storage system to reach the corresponding point according to the voltage probability distribution obtained in the step (b);
(d) And (c) constructing an optimal path navigation model of all the mobile energy storage systems by considering traffic flow data aiming at the route in the step (c).
(e) And (d) aiming at the navigation data in the step (d), taking the real-time load condition into consideration, and constructing an optimal power output generation model of the mobile energy storage system.
In summary, the invention provides a mobile energy storage scheduling method based on voltage sensitivity analysis. Firstly, calculating a daily optimal power flow scheduling scheme of the power distribution network according to load prediction data and the deployment condition of power generators of the power distribution network. And secondly, based on a scheduling scheme, carrying out voltage sensitivity analysis by considering a load prediction error and a topological structure of the power distribution network, and obtaining the voltage probability distribution of each node of the power distribution network under the prediction error.
Next, a future operational total route of the mobile energy storage system is generated in consideration of the node voltage threshold type, the node voltage threshold probability, the mobile energy storage state of charge, and the mobile energy storage time cost. And then, in a real-time stage, taking real-time traffic flow, fuel cost and time cost into consideration to perform real-time optimal path navigation of the mobile energy storage system, so as to ensure that the mobile energy storage system reaches a specified point to provide service. And finally, calculating the optimal output of the mobile energy storage system under the optimal power flow of the power distribution network based on the real-time load data, the deployment condition of the generator and the deployment condition of the mobile energy storage system.
Therefore, by adopting the mobile energy storage system scheduling method based on the voltage sensitivity analysis, the travel time of the mobile energy storage system can be reduced, the voltage distribution of the power distribution network can be improved, the influence of the error of load prediction on the stability of the power system can be reduced, and the destination of the mobile energy storage system can be reasonably arranged.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.

Claims (8)

1. The mobile energy storage system dispatching method based on voltage sensitivity analysis is characterized by comprising the following steps of:
s1, generating a day-ahead scheduling scheme of a power distribution network based on prediction data;
s2, aiming at the day-ahead scheduling scheme generated in the step S1, calculating probability distribution of voltage values of each node at each moment in consideration of prediction errors;
s3, aiming at probability distribution of the voltage values obtained in the step S2, generating a route of the mobile energy storage system for 24 hours in the future by taking the probability of voltage out-of-limit, the charge state of each mobile energy storage system and the time required for the mobile energy storage system to reach a corresponding point into consideration;
s4, aiming at the route in the step S3, considering traffic flow data, and constructing an optimal path navigation model of all the mobile energy storage systems;
s5, aiming at the optimal path navigation model constructed in the step S4, taking real-time load conditions into consideration, constructing an optimal power output generation model of the mobile energy storage system;
in step S1, a day-ahead scheduling scheme of the power distribution network is generated based on the prediction data, which specifically includes: the method comprises the steps of adopting predicted load data, considering original equipment of a power distribution network, and obtaining output of the original equipment of the power distribution network by utilizing an optimal power flow calculation model; the objective function of the optimal power flow calculation model is as follows:
（1）
wherein,Nrepresenting a collection of points in the distribution network equipped with generators,is an electric generatornRunning costs of->Representative generatornOutput power;
constraint conditions of the optimal power flow model are as follows:
(1) The voltage of a certain node is expressed as the voltage of the node adjacent to the certain node minus the voltage drop caused by the branch current on the branch; the non-convex node voltage transfer constraint is convex by removing the phase angles of the current and the voltage, reserving the amplitude and expressing the square of the current by a primary term:
（2）
wherein,v i representative nodeiA voltage amplitude;v j representative nodejA voltage amplitude;R ij is a nodeijResistance values therebetween;X ij is a nodeijReactance value between;P ij is a nodejInflow nodeiIs a power of (2);Q ij is a nodeiInflow nodejReactive power in between;l ij,t is a nodeijThe square of the current amplitude between them; omega is the set of grid nodes,i，jrepresenting nodes in the network;
(2) The power of the ingress node is equal to the power of the egress node; the power balance constraint is relaxed by splitting active power and reactive power:
（3）
（4）
wherein,active power for the inflow node; />Reactive power for the inflow node; />Slave nodeiOut to the nodekIs a power of (2); />Representing nodes in a networkiA collection of connected nodes; />Representing slave nodesjInflow to nodeiIs a power of (2); />Representative nodejiResistance values therebetween; />Representative nodejFlow direction nodeiIs the square of the current amplitude of (2); />Representing slave nodesiOut to the nodekIs set in the power domain; />Representing slave nodesjInflow to nodeiIs set in the power domain; />Representative nodejSum nodeiReactance value between;i，j，kall represent nodes in the network; />Is a nodeiThe output power of the generator;
(3) The square of the branch current is equal to the modular square of the apparent power divided by the node voltage; second order cone relaxation is carried out on branch power flow calculation constraint:
（5）
wherein,representing slave nodesiFlow direction nodejIs (1) the current of the (a)Squaring the amplitude;
(4) The node voltage should satisfy the voltage constraint:
（6）
wherein,representative nodeiA lower voltage limit of (2); />Representative nodeiUpper voltage limit of (2);
(5) The branch current should satisfy the current constraint:
（7）
wherein,representative nodeiTo the nodejAn upper limit of the square of the current magnitude of (2);
(6) The power distribution network generator should meet the generator output constraint:
（8）
wherein,representative nodeiThe upper power limit of the generator; />Representative nodeiA lower power limit of the generator;
in step S2, for the day-ahead scheduling scheme generated in step S1, a probability distribution of voltage values of each node at each time is calculated in consideration of a prediction error, including the steps of:
s21, calculating the variation of the voltage of the network node caused by the power variation;
the node connecting large power grid in power distribution network is called source node, and is used as letterSA representation; the node for observing the voltage change is called an observation node and is marked with lettersORepresenting, then observe the voltage at the nodeV O Expressed as the voltage at the source nodeV S A difference from a sum of voltage drops on all sides between the observation node and the source node; by kirchhoff's voltage law, the voltage at the observation node is expressed as:
（9）
wherein,U b representative is in the branchbVoltage drop of (2); omega shape branch Is a collection of edges between a source node and an observation node;
is arranged at the nodeiThe complex power of injection isS i At the nodeiThe voltage complex conjugate at isThe set of nodes between the source node and the observation node isN node The injection power of the intermediate node is changed to +.>The voltage of the intermediate node is changed to +.>Then observe the voltage variation of node +.>Expressed as:
（10）
wherein,representing the voltage value after the change of the observation node; />A complex conjugate representing a voltage change at the intermediate node; />Impedance between source node and observation node;
considering that the voltage phase angle change of the power distribution network is small, loosening the voltage in the equation, reserving amplitude information, and obtaining the upper limit of the node voltage change quantity of the power distribution network:
（11）
wherein,N action as a set of nodes of varying power,Z oi for the impedance shared between the source node to the action node and the observation node,representative nodeiPower variation of (2);
s22, calculating probability distribution of node voltage values;
considering that the error of the prediction system is normal distribution, and the influence of the active power and reactive power changes among different nodes is expressed as a covariance matrix; because the phase angle change of the power distribution network is small, the probability distribution of the voltage amplitude change is considered; the square of the amplitude of the voltage is expressed as the sum of squares of a real part and an imaginary part, and since the prediction error is normally distributed, the distribution of the square of the amplitude of the voltage is a weighted sum of squares of normal distribution and is expressed by gamma distribution; the probability of the node voltage change of the distribution network is calculated by the following formula:
（12）
wherein,a reference value representing a node voltage variation amount;βandθthe shape parameter and the scale parameter of the gamma distribution are calculated by the following formula:
（13）
wherein, the mathematical expectation and variance are the eigenvalues of the covariance matrixAnd->And (3) calculating to obtain:
（14）
（15）。
2. the method for dispatching a mobile energy storage system based on voltage sensitivity analysis according to claim 1, wherein in step S3, for the probability distribution of the voltage values obtained in step S2, a route of 24 hours in the future of the mobile energy storage system is generated by taking into account the probability of voltage out-of-limit, the state of charge of each mobile energy storage system, and the time required for the mobile energy storage system to reach the corresponding point, comprising the steps of:
s31, grouping out-of-limit points;
s32, calculating a set of points which can be reached by the mobile energy storage in fixed time;
s33, calculating the charge state of the mobile energy storage system;
s34, generating a total route of the mobile energy storage system.
3. The method for dispatching a mobile energy storage system based on voltage sensitivity analysis according to claim 2, wherein step S31 is specifically: and (2) calculating the probability of voltage out-of-limit of each node based on the node voltage probability density function obtained in the step (S2), and dividing the probability into two groups of points which are an upper limit point and a lower limit point.
4. The method for dispatching a mobile energy storage system based on voltage sensitivity analysis according to claim 3, wherein step S32 is specifically: constructing an optimal path selection model considering the shortest travel time, wherein the objective function of the model is as follows:
（16）
wherein,representing the time the mobile energy store navigates between destinations;
the constraint conditions of the optimal path selection model are as follows:
(1) The travel time of the mobile energy storage system between destinations is equal to the sum of the time it takes to walk through all road segments:
（17）
wherein,binary variables representing a selected section of the road network, which is then +.>The method comprises the steps of carrying out a first treatment on the surface of the When the mobile energy storage system does not pass through the road section ∈>；/>At the node for MESSijTime spent navigating in between;
(2) All road sections through which the mobile energy storage system passes should be connected end to end, and for a starting point, the mobile energy storage system can only exit from the point; for an intermediate node, the mobile energy storage system should only drive in to the point once and only drive out of the point once; for an endpoint, the mobile energy storage system can only exit the point once:
（18）
wherein,H t representing the start of the overall route;representing the end of the total route; />Representing a set of road network nodes; />For the binary variable of a road network selection section, when the mobile energy storage system passes the section, there is +.>The method comprises the steps of carrying out a first treatment on the surface of the When the mobile energy storage system does not pass through the road section ∈>；/>And->Is opposite to the direction of (3);
according to the obtained optimal path selection model, sequentially scanning road network nodes, and calculating the most of each nodeEndpoint set with short travel times less than 15 minutes and 30 minutes, recorded as D 15min And D 30min 。
5. The method for dispatching a mobile energy storage system based on voltage sensitivity analysis according to claim 4, wherein step S33 is specifically: the state of charge transfer equation of the mobile energy storage system is:
（19）
wherein,representing mobile energy storage systemmAt the moment of timetIs a state of charge of (2); />Representing mobile energy storage systemmAt the moment of timetIs a power output of (a);trepresenting a charging time of the mobile energy storage system; />Representing the maximum capacity of the mobile energy storage system battery;representing the aggregate of all mobile energy storage systems.
6. The method for dispatching a mobile energy storage system based on voltage sensitivity analysis according to claim 5, wherein step S34 is specifically: meanwhile, the following steps are executed by considering the high probability out-of-limit point of the power grid, the point which can be reached quickly by the mobile energy storage system and the charge state of each mobile energy storage system:
s341, respectively comparing the upper limit point and the lower limit point obtained in the step S31 with D 15min Taking the intersection to obtain selectable destinations of two groups of mobile energy storage systems which are divided into an upper limit and a lower limit; consider the extreme case, i.e. all mobile energy storage systemsTo be charged or discharged, if the number of points in the intersection is smaller than the number of the mobile energy storage systems, considering the point of easy out-of-limit of the power grid in the next period, and D 30min Taking the intersection as a supplement of the destination of the mobile energy storage system at the current moment; generating a selectable destination sequence of the mobile energy storage system in 24 hours by a method of preferentially selecting current nodes and supplementing future nodes;
s342, according to the selectable destination sequence obtained in the step S341, considering the real-time state of charge of the mobile energy storage system, and for the mobile energy storage system with the state of charge lower than 50%, selecting a node with the highest probability of exceeding the upper voltage limit in the selectable destination sequence as a destination; for a mobile energy storage system with a charge state higher than 50%, selecting a node with the highest probability of exceeding a lower voltage limit in an optional destination sequence as a destination; eventually a total route is generated for each mobile energy storage system for the next 24 hours.
7. The method for dispatching a mobile energy storage system based on voltage sensitivity analysis according to claim 6, wherein step S4 is specifically: according to the mobile energy storage total route obtained by calculation in the step S3, considering the influence of real-time traffic flow, comprehensively considering the minimized fuel cost and the time cost, constructing an online optimal path navigation model of the mobile energy storage system, and the objective function of the model is as follows:
（20）
wherein,fuel consumption for the mobile energy storage system; />Representing the time taken by the mobile energy storage system in providing power support; />Representing the time cost at the goalWeights in the function;
the partial constraint condition of the online optimal path navigation model of the mobile energy storage system is the same as the constraint condition of the optimal path selection model in the step S32, and the newly added constraint condition is as follows:
(1) The navigation time of the mobile energy storage system in each road section is affected by real-time traffic flow, and the navigation time of the traffic flow is considered to be expressed as a BRP model:
（21）
wherein the method comprises the steps ofRepresenting the navigation time under the influence of traffic flow; />Representing free sailing time of the mobile energy storage system under no influence of traffic flow; />Representing real-time traffic flow;d，b，Cis a preset parameter;
(2) The fuel cost of the mobile energy storage system is affected by the length of the sailing distance and the price of fuel oil:
（22）
wherein,representing the price of fuel; />Representing the amount of fuel consumed per kilometer; />Representing the length of each road segment in the network。
8. The method for dispatching a mobile energy storage system based on voltage sensitivity analysis according to claim 7, wherein step S5 is specifically: based on real-time load data, an optimal power output generation model of the mobile energy storage system is built, the output power of each mobile energy storage system is calculated, and an objective function of the model is as follows:
（23）
wherein,λcost of providing power support on behalf of the mobile energy storage system;representing at the nodeiMobile energy storage systemmOutput power of (2); />Representative generatornIs not limited by the operating cost of (a);
the partial constraint condition of the optimal power output generation model is the same as the optimal power flow calculation model in the step S1, and the newly added constraint condition is as follows:
(1) The power output of a mobile energy storage system will bring about a change in its state of charge:
（24）
(2) The output power of the mobile energy storage system should satisfy the power constraint:
（25）
wherein,for moving energy-storage systemsmLower power limit of (2); />For storing energy for movementmUpper power limit of (2); />For storing energy for movementmOutput power of (2);
(3) The power injection of the mobile energy storage system affects the power balance equation of the node:
（26）。
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